Hooke's Law

How many of us wondered how amazingly the objects behave when exposed to them?

For example, why is the fabric, if we stretch it in different directions, can drag on for a long time, and at once suddenly break? And why the same experiment is much more difficult to hold with a pencil? What determines the resistance of the material? How can you determine to what extent it is susceptible to deformation or stretching?

All these and many other questions more than 300 years ago, asked himself an English explorer Robert Hooke. And he found the answers now combined under the general title "Hooke's Law."

According to his research, each material has a so-called elasticity coefficient . This property allows the material to stretch within certain limits. The coefficient of elasticity is constant. This means that each material can withstand only a certain level of resistance, after which it reaches a level of irreversible deformation.

In general, Hooke's Law can be expressed by the formula:

F = k / x /,

Where F is the elastic force, k is the already mentioned elasticity coefficient, and / x / is the change in the length of the material. What is meant by the change in this indicator? Under the influence of force, a certain studied object, whether it is a string, rubber or any other, changes, stretching or shrinking. The change in length in this case is the difference between the original and final length of the studied object. That is, by how much the spring has stretched / contracted (rubber, string, etc.)

Hence, knowing the length and the constant elasticity coefficient for a given material, one can find the force with which the material is stretched, or the force of elasticity, as Hooke's Law is often called.

There are also special cases in which this law can not be used in its standard form. It is about measuring the force of deformation under shearing conditions, that is, in situations where a deformation is produced by a certain force acting on the material at an angle. Hooke's law under shear can be expressed thus:

Τ = Gy,

Where τ is the required force, G is a constant coefficient known as the shear modulus, y is the shear angle, the value by which the tilt angle of the object has changed.

The linear elastic force (Hooke's Law) is applicable only under conditions of small contractions and strains. If, however, the force continues to affect the studied object, then there comes a point when it loses its elasticity qualities, that is, reaches its elasticity limit. The force exerted exceeds the resistance force. Technically, this can be seen not only as a change in the visible parameters of the material, but also as a reduction in its resistance. The force required to change the material is now reduced. In such cases, the properties of the object change, that is, the body is no longer able to resist. In ordinary life, we see that it tears, breaks, bursts, etc. Not necessarily, of course, a violation of integrity, but the quality while suffering significantly. And the coefficient of elasticity, which is valid for a material or body in undistorted form, ceases to be significant in the form of a distorted one.

This case allows us to say that the linear system (directly proportional to the dependence of one parameter on the other) became nonlinear when the interdependence of the parameters is lost, and the change occurs on a different basis.

On the basis of such observations, Thomas Jung created the elasticity modulus formula, which was later named in his honor and became the basis for creating the Theory of Elasticity. The modulus of elasticity allows one to consider deformation in cases when the changes in elasticity are significant. The law has the form:

E = σ / η,

Where σ is the force applied to the transverse cross-sectional area of the body, η is the modulus of elongation or contraction of the body, E is the modulus of elasticity determining the degree of stretching or contraction of the body under the influence of mechanical stress.